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Saturation estimates for hp-finite element methods


Bank, Randolph E; Parsania, Asieh; Sauter, Stefan A (2013). Saturation estimates for hp-finite element methods. Computing and Visualization in Science, 16(5):195-217.

Abstract

In this paper we will prove saturation estimates for the adaptive (Formula presented.)-finite element method for linear, second order partial differential equations. More specifically we will consider a sequence of nested finite element discretizations where we allow for both, local mesh refinement and locally increasing the polynomial order. We will prove that the energy norm of the error on the finer level can be estimated by the sum of a contraction of the old error and data oscillations. We will derive estimates of the contraction factor which are explicit with respect to the local mesh width and the local polynomial degree. In order to cover (Formula presented.)-refinement of finite element spaces new polynomial projection operators will be introduced and new polynomial inverse estimates will be derived.

Abstract

In this paper we will prove saturation estimates for the adaptive (Formula presented.)-finite element method for linear, second order partial differential equations. More specifically we will consider a sequence of nested finite element discretizations where we allow for both, local mesh refinement and locally increasing the polynomial order. We will prove that the energy norm of the error on the finer level can be estimated by the sum of a contraction of the old error and data oscillations. We will derive estimates of the contraction factor which are explicit with respect to the local mesh width and the local polynomial degree. In order to cover (Formula presented.)-refinement of finite element spaces new polynomial projection operators will be introduced and new polynomial inverse estimates will be derived.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:27 February 2013
Deposited On:27 Jan 2016 09:51
Last Modified:16 Feb 2018 20:07
Publisher:Springer
ISSN:1432-9360
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00791-015-0234-2

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